Elliptic curve isogeny class with Cremona label 8670e (LMFDB label 8670.g)

• Label: 8670e
• Number of curves: $8$
• Conductor: $8670$
• CM: no
• Rank: $0$

Elliptic curves in class 8670e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8670.g8	8670e1	\([1, 1, 0, 428, 10624]\)	\(357911/2160\)	\(-52137149040\)	\([2]\)	\(9216\)	\(0.73832\)	\(\Gamma_0(N)\)-optimal
8670.g6	8670e2	\([1, 1, 0, -5352, 134316]\)	\(702595369/72900\)	\(1759628780100\)	\([2, 2]\)	\(18432\)	\(1.0849\)
8670.g7	8670e3	\([1, 1, 0, -3907, -309299]\)	\(-273359449/1536000\)	\(-37075305984000\)	\([2]\)	\(27648\)	\(1.2876\)
8670.g5	8670e4	\([1, 1, 0, -19802, -932094]\)	\(35578826569/5314410\)	\(128276938069290\)	\([2]\)	\(36864\)	\(1.4315\)
8670.g4	8670e5	\([1, 1, 0, -83382, 9232614]\)	\(2656166199049/33750\)	\(814642953750\)	\([2]\)	\(36864\)	\(1.4315\)
8670.g3	8670e6	\([1, 1, 0, -96387, -11536371]\)	\(4102915888729/9000000\)	\(217238121000000\)	\([2, 2]\)	\(55296\)	\(1.6342\)
8670.g1	8670e7	\([1, 1, 0, -1541387, -737215371]\)	\(16778985534208729/81000\)	\(1955143089000\)	\([2]\)	\(110592\)	\(1.9808\)
8670.g2	8670e8	\([1, 1, 0, -131067, -2540379]\)	\(10316097499609/5859375000\)	\(141431068359375000\)	\([2]\)	\(110592\)	\(1.9808\)

Rank

The elliptic curves in class 8670e have rank \(0\).

Complex multiplication

The elliptic curves in class 8670e do not have complex multiplication.

Modular form 8670.2.a.e

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.